Mr. Williams is currently en route to the Middle East and is expected to start holding meetings on Thursday with senior Israeli and Palestinian officials, UN spokesperson Michele Montas told journalists today.
Mr. Williams is then scheduled to travel to the Egyptian capital, Cairo, for further consultations.
Yesterday Mr. Ban's spokesperson issued a statement voicing hope that the ceasefire reached among the Palestinian factions will hold after a week of deadly clashes in the Gaza Strip.
The statement also expressed deep concern that Palestinian militants continue to fire rockets targeting Israeli civilians, and, while recognizing Israel's right to defend itself, that Israeli military operations in Gaza have led to a mounting number of civilian casualties.
Last week Mr. Ban announced that Mr. Williams had been appointed as the UN Special Coordinator for the Middle East Peace Process, as well as the Secretary-General's Personal Representative to the Palestine Liberation Organization and the Palestinian Authority and his Envoy to the Quartet, the international diplomatic grouping on the Middle East.